ACR X UNAUTH CLB TO OCCUPIED ALT HAD LTSS FROM ACR Y.

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ACR X A B-727 AND HAD JUST DEPARTED MLI FOR A 1 HR 20 MIN FLT TO ICT. WE WERE STEP CLBED UP TO FL280 AND WERE EXPECTING FURTHER CLB CLRNC TO FL310 SHORTLY. CLBING THROUGH FL270 WE WERE ADVISED TO LEVEL OFF AT FL280 BECAUSE OF XING TFC. AS WE WERE LEVELING OFF AT FL280 THE CTLR COMES BACK ON THE RADIO AND SAYS; 'ACR X TFC 12 O'CLOCK FL290. HIGHER WHEN CLR.' EXPECTING A FURTHER CLB CLRNC; BOTH THE CAPT AND I THOUGHT THAT THE CTLR SAID; 'ACR X; CLB FL290; HIGHER WHEN CLR OF TFC.' THE CAPT REPLIED 'FL290; ACR X.' THE CAPT THEN SET 29000 FT IN THE ALT ALERT WINDOW AND I PROCEEDED TO CLB TO FL290. AS WE REACHED FL290 THE CTLR TOLD US TO DSND BACK TO FL280. OBVIOUSLY; WE HAD GOTTEN VERY CLOSE TO THE XING TFC. I REALIZE THAT THIS CLOSE CALL WAS OUR FAULT. WE HEARD WHAT WE EXPECTED THE NEXT CLRNC TO BE. HOWEVER; I ALSO THINK THAT THE CTLR BEARS SOME OF THE RESPONSIBILITY. HE ADVISED US OF THE TFC WE REPEATED BACK AN ALT. THE NEXT HIGHER ALT WE WERE EXPECTING TO GET CLRED TO (FL290). IT IS HIGHLY UNUSUAL FOR A CREW TO REPEAT THE POS (12 O'CLOCK OR 3 O'CLOCK) OR THE ALT OF ADVISED TFC BACK TO A CTLR. IT IS; HOWEVER; NOT AT ALL UNUSUAL FOR A CREW TO RPT A NEW ALT TO WHICH THEY ARE CLRED BACK TO A CTLR. HEARING OUR RESPONSE OF 'FL290; ACR X.' THE CTLR SHOULD HAVE VERIFIED FOR US NOT TO CLB TO FL290 BUT THAT OUR TFC IS AT FL290. SUPPLEMENTAL INFO FROM ACN 286053: I HAD ZAU STOP ACR X AT FL280 FOR ACR Y. A FEW MINS LATER; ACR X CHKED ON AND WAS INFORMED '4 MINS' FOR HIGHER. I CALLED TFC TO ACR Y AND SHIPPED HIM TO ZAU. A MIN LATER; I CALLED TFC TO X; 'TFC AT YOUR 12 O'CLOCK 15 MI NEBOUND FL290; HIGHER WHEN YOU'RE CLR.' SHORTLY AFTER THAT; I NOTICED X OUT OF FL283 CLBING. I INSTRUCTED X TO MAINTAIN FL280. I INFORMED THE SUPVR AND WAS RELIEVED FROM THE SECTOR.